However, well-known negative results demonstrate the difficulty of aggregating preferences to a social choice with only ordinal utility functions available. Arrow's general impossibility theorem is one of the central insights, showing that it is impossible to have a social welfare function that satisfies a certain set of apparently reasonable conditions [1]}. Based on this impossibility, [2]} and [3]} showed that no (non-dictatorial) mechanism with more than two possible outcomes is dominant-strategy incentive-compatible (aka. strategy-proof). The limitations of deterministic mechanisms led to significant attention for probabilistic social choice more recently [4]}.
